Kolmogorov complexity and its applications

我对开发一个令人信服的大数据理论很感兴趣。这样的理论将取决于科尔莫戈罗夫的复杂性和信息距离。柯尔莫戈罗夫复杂性是在一个对象上定义的。在两个对象上定义了信息距离[C.Bennett，P.Gacs，M.Li，P.Vitanyi，W.Zurek，Information Distance，IEEE Tran-IT，44：4(1998)]。这个概念可以推广到许多对象。使用这样的理论，通常可以最佳地近似两段数据的“语义距离”或接近这一直观概念。这一理论的关键是对数据进行压缩。将研究许多压缩数据的方法，包括错误编码、聚类，特别是深度神经网络。深度神经网络可以被认为是压缩数据，特别是大数据的方法。以下短期目标与本研究的上述主题一致：

I am interested in developing a compelling theory of big data. Such a theory will depend on Kolmogorov complexity and information distance. Kolmogorov complexity is defined on one object. Information distance [C. Bennett, P. Gacs, M. Li, P. Vitanyi, W. Zurek, Information distance, IEEE Tran-IT, 44:4(1998)] is defined on two objects. This concept can be generalized to many objects. Using such a theory it is possible to optimally approximate the intuitive concept of "semantic distance" or closeness of two piece of data, in general. The key to this theory is to compress the data. Many ways of compressing data will be studied, including error encoding, clustering, and especially deep neural networks. Deep neural networks can be considered as ways of compressing data, especially big data. The following short-term goals are in tune with the above main theme of this research: